著者

Tatsuya KOYAKUMARU Masahiro YUKAWA Eduardo PAVEZ Antonio ORTEGA

出版者

The Institute of Electronics, Information and Communication Engineers

雑誌

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences (ISSN:09168508)

巻号頁・発行日

vol.E106-A, no.1, pp.23-34, 2023-01-01

被引用文献数

3

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This paper presents a convex-analytic framework to learn sparse graphs from data. While our problem formulation is inspired by an extension of the graphical lasso using the so-called combinatorial graph Laplacian framework, a key difference is the use of a nonconvex alternative to the l1 norm to attain graphs with better interpretability. Specifically, we use the weakly-convex minimax concave penalty (the difference between the l1 norm and the Huber function) which is known to yield sparse solutions with lower estimation bias than l1 for regression problems. In our framework, the graph Laplacian is replaced in the optimization by a linear transform of the vector corresponding to its upper triangular part. Via a reformulation relying on Moreau's decomposition, we show that overall convexity is guaranteed by introducing a quadratic function to our cost function. The problem can be solved efficiently by the primal-dual splitting method, of which the admissible conditions for provable convergence are presented. Numerical examples show that the proposed method significantly outperforms the existing graph learning methods with reasonable computation time.